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Diophantine Analysis

Joern Steuding

1 ratings by Goodreads
ISBN 10: 1584884827 / ISBN 13: 9781584884828
Published by Chapman and Hall/CRC, 2005
New Condition: New
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Bibliographic Details

Title: Diophantine Analysis

Publisher: Chapman and Hall/CRC

Publication Date: 2005

Binding: HRD

Book Condition:New

About this title

Synopsis:

While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number theory. Many diophantine problems have simple formulations, they can be extremely difficult to attack, and many open problems and conjectures remain.

Diophantine Analysis examines the theory of diophantine approximations and the theory of diophantine equations, with emphasis on interactions between these subjects. Beginning with the basic principles, the author develops his treatment around the theory of continued fractions and examines the classic theory, including some of its applications. He also explores modern topics rarely addressed in other texts, including the abc conjecture, the polynomial Pell equation, and the irrationality of the zeta function and touches on topics and applications related to discrete mathematics, such as factoring methods for large integers.

Setting the stage for tackling the field's many open problems and conjectures, Diophantine Analysis is an ideal introduction to the fundamentals of this venerable but still dynamic field. A detailed appendix supplies the necessary background material, more than 200 exercises reinforce the concepts, and engaging historical notes bring the subject to life.

Review:

This nicely written textbook provides a down-to-earth introduction to various aspects of Diophantine approximations, transcendence, theory and Diophantine equations....I would not hesitate to recommend this book to anybody wishing to learn something about Diophantine analysis...
Mathematical Reviews, Issue 2006a

The book offers a nice introduction to fundamentals of number theory with the emphasis of Diophantine analysis and Diophantine approximation and their mutual interactions. ...The reader finds many interesting basic principles and results, which can be used as a springboard to a deeper study of the subject. ...The book is written in a lively and lucid style and is principally self-contained and requires only standard mathematical background. It is thus directed not only to graduate or advanced undergraduate students, but to everybody interest in this important part of number theory.
-EMS Newsletter, March 2006

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